"Green guardian" volunteers who clean up and maintain local parks, allotments and cemeteries should be rewarded with council tax rebates, a thinktank has recommended.

Policy Exchange put forward the idea in a paper with other proposals to improve local green spaces amid warnings that Britain's parks are close to crisis because of spending cuts.

On average local authority spending on open spaces was cut by 10.5% between 2010/11 and 2012/13, said the thinktank, and there is no ringfence protecting the budget spent on maintaining green spaces. Combined with the increasing demand for housing and other urban development there is a risk that the UK's parks will deteriorate or become spaces that are the preserve of the wealthy.

The rebate could be worth as much as £1,500 a year, the average amount of council tax paid. Local authorities could set the discount rate themselves, basing it on hours spent volunteering or setting a minimum number of hours necessary for volunteers to qualify for the rebate. This would not only provide a solution to the declining number of park rangers but would encourage people to get involved in their local communities, said Policy Exchange.

"Britain's parks are the lungs of our great cities," said Katherine Drayson, author of the report. "However, as local authority budgets have been squeezed, public funding on parks, cemeteries and allotments has declined sharply. The time has come for radical new thinking to safeguard our parks and make them more accessible to everyone in society … a "green guardian" scheme that rewards local volunteers to help maintain their local parks with council tax rebates is just one way of protecting and enhancing our public green spaces."

Policy Exchange also suggested that the Department of Health runs a series of pilots allowing GPs to refer patients to non-clinical sources of support, such as physical fitness classes held in a local park. The patient would pay the standard prescription charge and the clinical commissioning group would fund the remainder of the course.

Campaigners have warned that Britain's parks are close to crisis point, because of budget cuts and staff losses and in some cases being sold off. A report from the Heritage Lottery Fund in June said 86% of parks managers have seen cuts to their budgets since 2010, a trend they expect to continue over the next three years. The fund said almost half of local authorities (46%) were considering selling parks and green spaces or transferring their management to others, which could lead to the loss of part or all of some parks.